Maximum Matching in General Graphs Without Explicit Consideration of Blossoms Revisited

Maximum Matching in General Graphs Without Explicit Consideration of Blossoms Revisited

We reduce the problem of finding an augmenting path in a general graph to a reachability problem in a directed bipartite graph. A slight modification of depth-first search leads to an algorithm for finding such paths. Although this setting is equivalent to the traditional terminology of blossoms due...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2015-09
1. Verfasser: Blum, Norbert
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Graph matching
Graph theory
Graphs
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Blum, Norbert
description We reduce the problem of finding an augmenting path in a general graph to a reachability problem in a directed bipartite graph. A slight modification of depth-first search leads to an algorithm for finding such paths. Although this setting is equivalent to the traditional terminology of blossoms due to Edmonds, there are some advantages. Mainly, this point of view enables the description of algorithms for the solution of matching problems without explicit analysis of blossoms, nested blossoms, and so on. Exemplary, we describe an efficient realization of the Hopcroft-Karp approach for the computation of a maximum cardinality matching in general graphs and a variant of Edmonds' primal-dual algorithm for the maximum weighted matching problem.
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2083134439</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2083134439</sourcerecordid><originalsourceid>FETCH-proquest_journals_20831344393</originalsourceid><addsrcrecordid>eNqNysEKgkAUQNEhCJLyHx60FnRGy7aJ2cZNBC5l0DGf6Iz5xvDzc9EHtLqLezbM4UIEXhxyvmMuUef7Pj-deRQJhxW5XHCYB8ilrVrUL0ANmdJqkj1kkxxbggJta2YL6TL2WKGFxGjCeiUWjQbTwLU3RGYgeKgPElpVH9i2kT0p99c9O97SZ3L3xsm8Z0W27Mw86XWV3I9FIMJQXMR_6gtk0EHH</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2083134439</pqid></control><display><type>article</type><title>Maximum Matching in General Graphs Without Explicit Consideration of Blossoms Revisited</title><source>Free E- Journals</source><creator>Blum, Norbert</creator><creatorcontrib>Blum, Norbert</creatorcontrib><description>We reduce the problem of finding an augmenting path in a general graph to a reachability problem in a directed bipartite graph. A slight modification of depth-first search leads to an algorithm for finding such paths. Although this setting is equivalent to the traditional terminology of blossoms due to Edmonds, there are some advantages. Mainly, this point of view enables the description of algorithms for the solution of matching problems without explicit analysis of blossoms, nested blossoms, and so on. Exemplary, we describe an efficient realization of the Hopcroft-Karp approach for the computation of a maximum cardinality matching in general graphs and a variant of Edmonds' primal-dual algorithm for the maximum weighted matching problem.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algorithms ; Graph matching ; Graph theory ; Graphs</subject><ispartof>arXiv.org, 2015-09</ispartof><rights>2015. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>780,784</link.rule.ids></links><search><creatorcontrib>Blum, Norbert</creatorcontrib><title>Maximum Matching in General Graphs Without Explicit Consideration of Blossoms Revisited</title><title>arXiv.org</title><description>We reduce the problem of finding an augmenting path in a general graph to a reachability problem in a directed bipartite graph. A slight modification of depth-first search leads to an algorithm for finding such paths. Although this setting is equivalent to the traditional terminology of blossoms due to Edmonds, there are some advantages. Mainly, this point of view enables the description of algorithms for the solution of matching problems without explicit analysis of blossoms, nested blossoms, and so on. Exemplary, we describe an efficient realization of the Hopcroft-Karp approach for the computation of a maximum cardinality matching in general graphs and a variant of Edmonds' primal-dual algorithm for the maximum weighted matching problem.</description><subject>Algorithms</subject><subject>Graph matching</subject><subject>Graph theory</subject><subject>Graphs</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNysEKgkAUQNEhCJLyHx60FnRGy7aJ2cZNBC5l0DGf6Iz5xvDzc9EHtLqLezbM4UIEXhxyvmMuUef7Pj-deRQJhxW5XHCYB8ilrVrUL0ANmdJqkj1kkxxbggJta2YL6TL2WKGFxGjCeiUWjQbTwLU3RGYgeKgPElpVH9i2kT0p99c9O97SZ3L3xsm8Z0W27Mw86XWV3I9FIMJQXMR_6gtk0EHH</recordid><startdate>20150916</startdate><enddate>20150916</enddate><creator>Blum, Norbert</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20150916</creationdate><title>Maximum Matching in General Graphs Without Explicit Consideration of Blossoms Revisited</title><author>Blum, Norbert</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20831344393</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Algorithms</topic><topic>Graph matching</topic><topic>Graph theory</topic><topic>Graphs</topic><toplevel>online_resources</toplevel><creatorcontrib>Blum, Norbert</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Access via ProQuest (Open Access)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Blum, Norbert</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Maximum Matching in General Graphs Without Explicit Consideration of Blossoms Revisited</atitle><jtitle>arXiv.org</jtitle><date>2015-09-16</date><risdate>2015</risdate><eissn>2331-8422</eissn><abstract>We reduce the problem of finding an augmenting path in a general graph to a reachability problem in a directed bipartite graph. A slight modification of depth-first search leads to an algorithm for finding such paths. Although this setting is equivalent to the traditional terminology of blossoms due to Edmonds, there are some advantages. Mainly, this point of view enables the description of algorithms for the solution of matching problems without explicit analysis of blossoms, nested blossoms, and so on. Exemplary, we describe an efficient realization of the Hopcroft-Karp approach for the computation of a maximum cardinality matching in general graphs and a variant of Edmonds' primal-dual algorithm for the maximum weighted matching problem.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2015-09
issn 2331-8422
language eng
recordid cdi_proquest_journals_2083134439
source Free E- Journals
subjects Algorithms
Graph matching
Graph theory
Graphs
title Maximum Matching in General Graphs Without Explicit Consideration of Blossoms Revisited
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-03T18%3A25%3A23IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Maximum%20Matching%20in%20General%20Graphs%20Without%20Explicit%20Consideration%20of%20Blossoms%20Revisited&rft.jtitle=arXiv.org&rft.au=Blum,%20Norbert&rft.date=2015-09-16&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2083134439%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2083134439&rft_id=info:pmid/&rfr_iscdi=true